Problem: Simplify the following expression: $ q = \dfrac{-5}{-9z - 3} + \dfrac{10}{7} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{-5}{-9z - 3} \times \dfrac{7}{7} = \dfrac{-35}{-63z - 21} $ Multiply the second expression by $\dfrac{-9z - 3}{-9z - 3}$ $ \dfrac{10}{7} \times \dfrac{-9z - 3}{-9z - 3} = \dfrac{-90z - 30}{-63z - 21} $ Therefore $ q = \dfrac{-35}{-63z - 21} + \dfrac{-90z - 30}{-63z - 21} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{-35 - 90z - 30}{-63z - 21} $ $q = \dfrac{-90z - 65}{-63z - 21}$ Simplify the expression by dividing the numerator and denominator by -1: $q = \dfrac{90z + 65}{63z + 21}$